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Math Help - Simple national Income Models

  1. #1
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    Simple national Income Models

    I'm not overly concerned what the answer to this is however I would appreciate it greatly if someone could at least point me in the correct direction as I am currently cluelessly !!!!

    A simple national income model is given by
    Y = C + I* + G*
    C = a + bY (a > 0 and 0 < b < 1)
    for some constants a and b and where I*, G* are exogenous variables.

    Find the equilibrium solution for Y and C, and hence deduce the multiplier for G* on C.
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  2. #2
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    Subsititute C = a + bY into the first expression.

    Y = a + bY + I + G

    Y(1-b) = a + I + G

    Y = \frac{a + I + G}{1-b}

    So an increase of 1 to G will cause an increase of \frac{1}{1-b} in Y. Hence the multiplier is \frac{1}{1-b}



    Why is this an equilibrium?
    if you are interested in understanding this; You can think of the model as trying to find a level of national production (Y) at which there is exactly enough demand (C + I + G) to consume the production.
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  3. #3
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    Quote Originally Posted by SpringFan25 View Post
    Subsititute C = a + bY into the first expression.

    Y = a + bY + I + G

    Y(1-b) = a + I + G

    Y = \frac{a + I + G}{1-b}

    So an increase of 1 to G will cause an increase of \frac{1}{1-b} in Y. Hence the multiplier is \frac{1}{1-b}



    Why is this an equilibrium?
    if you are interested in understanding this; You can think of the model as trying to find a level of national production (Y) at which there is exactly enough demand (C + I + G) to consume the production.
    I cant believe it was that easy...I got to that point by substitution and what not but couldnt deduce the multiplier....numpty or what! cheers mate
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